Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5292,2,Mod(1,5292)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5292, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5292.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5292.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(42.2568327497\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.321.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 756) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.69963\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5292.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.28799 | −1.91765 | −0.958824 | − | 0.284000i | \(-0.908338\pi\) | ||||
−0.958824 | + | 0.284000i | \(0.908338\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.81089 | −1.14903 | −0.574514 | − | 0.818495i | \(-0.694809\pi\) | ||||
−0.574514 | + | 0.818495i | \(0.694809\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.28799 | 0.911925 | 0.455962 | − | 0.889999i | \(-0.349295\pi\) | ||||
0.455962 | + | 0.889999i | \(0.349295\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.810892 | −0.196670 | −0.0983351 | − | 0.995153i | \(-0.531352\pi\) | ||||
−0.0983351 | + | 0.995153i | \(0.531352\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.09888 | 1.62860 | 0.814298 | − | 0.580447i | \(-0.197122\pi\) | ||||
0.814298 | + | 0.580447i | \(0.197122\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.47710 | −1.35057 | −0.675284 | − | 0.737557i | \(-0.735979\pi\) | ||||
−0.675284 | + | 0.737557i | \(0.735979\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.3869 | 2.67738 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.81089 | 0.707665 | 0.353832 | − | 0.935309i | \(-0.384878\pi\) | ||||
0.353832 | + | 0.935309i | \(0.384878\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.28799 | 0.590541 | 0.295270 | − | 0.955414i | \(-0.404590\pi\) | ||||
0.295270 | + | 0.955414i | \(0.404590\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.76509 | −0.947775 | −0.473888 | − | 0.880585i | \(-0.657150\pi\) | ||||
−0.473888 | + | 0.880585i | \(0.657150\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.09888 | 0.327791 | 0.163895 | − | 0.986478i | \(-0.447594\pi\) | ||||
0.163895 | + | 0.986478i | \(0.447594\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.76509 | −1.33666 | −0.668332 | − | 0.743863i | \(-0.732991\pi\) | ||||
−0.668332 | + | 0.743863i | \(0.732991\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.33379 | 0.486284 | 0.243142 | − | 0.969991i | \(-0.421822\pi\) | ||||
0.243142 | + | 0.969991i | \(0.421822\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.86398 | 1.35492 | 0.677461 | − | 0.735559i | \(-0.263080\pi\) | ||||
0.677461 | + | 0.735559i | \(0.263080\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16.3411 | 2.20343 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.47710 | 0.452680 | 0.226340 | − | 0.974048i | \(-0.427324\pi\) | ||||
0.226340 | + | 0.974048i | \(0.427324\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.95420 | 0.762357 | 0.381179 | − | 0.924501i | \(-0.375518\pi\) | ||||
0.381179 | + | 0.924501i | \(0.375518\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −14.0989 | −1.74875 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.52290 | −0.430391 | −0.215195 | − | 0.976571i | \(-0.569039\pi\) | ||||
−0.215195 | + | 0.976571i | \(0.569039\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.05308 | 0.718369 | 0.359184 | − | 0.933267i | \(-0.383055\pi\) | ||||
0.359184 | + | 0.933267i | \(0.383055\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.3869 | −1.21569 | −0.607846 | − | 0.794055i | \(-0.707966\pi\) | ||||
−0.607846 | + | 0.794055i | \(0.707966\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.14468 | −0.578822 | −0.289411 | − | 0.957205i | \(-0.593459\pi\) | ||||
−0.289411 | + | 0.957205i | \(0.593459\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.71201 | −0.187917 | −0.0939586 | − | 0.995576i | \(-0.529952\pi\) | ||||
−0.0939586 | + | 0.995576i | \(0.529952\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.47710 | 0.377144 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.5302 | 1.32820 | 0.664098 | − | 0.747645i | \(-0.268816\pi\) | ||||
0.664098 | + | 0.747645i | \(0.268816\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −30.4400 | −3.12307 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.04580 | 0.106185 | 0.0530925 | − | 0.998590i | \(-0.483092\pi\) | ||||
0.0530925 | + | 0.998590i | \(0.483092\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.9098 | 1.78209 | 0.891045 | − | 0.453916i | \(-0.149973\pi\) | ||||
0.891045 | + | 0.453916i | \(0.149973\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.00000 | −0.689730 | −0.344865 | − | 0.938652i | \(-0.612075\pi\) | ||||
−0.344865 | + | 0.938652i | \(0.612075\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.90112 | −0.667156 | −0.333578 | − | 0.942722i | \(-0.608256\pi\) | ||||
−0.333578 | + | 0.942722i | \(0.608256\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.62178 | −0.538469 | −0.269235 | − | 0.963075i | \(-0.586771\pi\) | ||||
−0.269235 | + | 0.963075i | \(0.586771\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −20.1520 | −1.89574 | −0.947869 | − | 0.318661i | \(-0.896767\pi\) | ||||
−0.947869 | + | 0.318661i | \(0.896767\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 27.7738 | 2.58992 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.52290 | 0.320264 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −35.9629 | −3.21662 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.14468 | −0.190310 | −0.0951550 | − | 0.995462i | \(-0.530335\pi\) | ||||
−0.0951550 | + | 0.995462i | \(0.530335\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.38688 | −0.295913 | −0.147956 | − | 0.988994i | \(-0.547270\pi\) | ||||
−0.147956 | + | 0.988994i | \(0.547270\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.9542 | −1.10675 | −0.553376 | − | 0.832932i | \(-0.686661\pi\) | ||||
−0.553376 | + | 0.832932i | \(0.686661\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.2880 | −1.46635 | −0.733174 | − | 0.680041i | \(-0.761962\pi\) | ||||
−0.733174 | + | 0.680041i | \(0.761962\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.5302 | −1.04783 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.3411 | −1.35705 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.56870 | −0.128513 | −0.0642565 | − | 0.997933i | \(-0.520468\pi\) | ||||
−0.0642565 | + | 0.997933i | \(0.520468\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.38688 | −0.112862 | −0.0564312 | − | 0.998406i | \(-0.517972\pi\) | ||||
−0.0564312 | + | 0.998406i | \(0.517972\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.0989 | −1.13245 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.8640 | −1.34589 | −0.672946 | − | 0.739692i | \(-0.734971\pi\) | ||||
−0.672946 | + | 0.739692i | \(0.734971\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.2967 | 1.35478 | 0.677389 | − | 0.735625i | \(-0.263111\pi\) | ||||
0.677389 | + | 0.735625i | \(0.263111\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.9556 | −1.07991 | −0.539957 | − | 0.841692i | \(-0.681560\pi\) | ||||
−0.539957 | + | 0.841692i | \(0.681560\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.18911 | −0.168393 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.14331 | 0.695153 | 0.347576 | − | 0.937652i | \(-0.387005\pi\) | ||||
0.347576 | + | 0.937652i | \(0.387005\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.0617 | 1.27525 | 0.637627 | − | 0.770345i | \(-0.279916\pi\) | ||||
0.637627 | + | 0.770345i | \(0.279916\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.4400 | −1.22197 | −0.610986 | − | 0.791641i | \(-0.709227\pi\) | ||||
−0.610986 | + | 0.791641i | \(0.709227\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 24.7207 | 1.81750 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.09022 | 0.225980 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.96286 | 0.214385 | 0.107193 | − | 0.994238i | \(-0.465814\pi\) | ||||
0.107193 | + | 0.994238i | \(0.465814\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.4313 | −1.25473 | −0.627366 | − | 0.778724i | \(-0.715867\pi\) | ||||
−0.627366 | + | 0.778724i | \(0.715867\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.2880 | 0.732989 | 0.366495 | − | 0.930420i | \(-0.380558\pi\) | ||||
0.366495 | + | 0.930420i | \(0.380558\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.00000 | −0.496217 | −0.248108 | − | 0.968732i | \(-0.579809\pi\) | ||||
−0.248108 | + | 0.968732i | \(0.579809\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.00000 | −0.628587 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −27.0531 | −1.87130 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.4327 | 1.13127 | 0.565636 | − | 0.824655i | \(-0.308631\pi\) | ||||
0.565636 | + | 0.824655i | \(0.308631\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 37.5846 | 2.56325 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.66621 | −0.179349 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.13602 | 0.276969 | 0.138484 | − | 0.990365i | \(-0.455777\pi\) | ||||
0.138484 | + | 0.990365i | \(0.455777\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.2967 | −1.41351 | −0.706754 | − | 0.707459i | \(-0.749841\pi\) | ||||
−0.706754 | + | 0.707459i | \(0.749841\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.85532 | −0.386930 | −0.193465 | − | 0.981107i | \(-0.561973\pi\) | ||||
−0.193465 | + | 0.981107i | \(0.561973\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.04580 | −0.527098 | −0.263549 | − | 0.964646i | \(-0.584893\pi\) | ||||
−0.263549 | + | 0.964646i | \(0.584893\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.2953 | −0.932521 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.0989 | −0.911981 | −0.455991 | − | 0.889985i | \(-0.650715\pi\) | ||||
−0.455991 | + | 0.889985i | \(0.650715\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.7280 | −1.72170 | −0.860849 | − | 0.508860i | \(-0.830067\pi\) | ||||
−0.860849 | + | 0.508860i | \(0.830067\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.3411 | 1.48516 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.43268 | 0.153549 | 0.0767746 | − | 0.997048i | \(-0.475538\pi\) | ||||
0.0767746 | + | 0.997048i | \(0.475538\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.6835 | 1.55184 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.5302 | −0.781611 | −0.390806 | − | 0.920473i | \(-0.627804\pi\) | ||||
−0.390806 | + | 0.920473i | \(0.627804\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.90112 | −0.425541 | −0.212771 | − | 0.977102i | \(-0.568249\pi\) | ||||
−0.212771 | + | 0.977102i | \(0.568249\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −42.2967 | −2.59826 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.8109 | 1.32983 | 0.664917 | − | 0.746917i | \(-0.268467\pi\) | ||||
0.664917 | + | 0.746917i | \(0.268467\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.52290 | 0.456984 | 0.228492 | − | 0.973546i | \(-0.426621\pi\) | ||||
0.228492 | + | 0.973546i | \(0.426621\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −51.0159 | −3.07638 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.23491 | 0.554872 | 0.277436 | − | 0.960744i | \(-0.410515\pi\) | ||||
0.277436 | + | 0.960744i | \(0.410515\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.6749 | −0.815774 | −0.407887 | − | 0.913032i | \(-0.633734\pi\) | ||||
−0.407887 | + | 0.913032i | \(0.633734\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.14331 | 0.127406 | 0.0637032 | − | 0.997969i | \(-0.479709\pi\) | ||||
0.0637032 | + | 0.997969i | \(0.479709\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3425 | −0.961321 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.29665 | 0.543116 | 0.271558 | − | 0.962422i | \(-0.412461\pi\) | ||||
0.271558 | + | 0.962422i | \(0.412461\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.9098 | −0.868081 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −21.2967 | −1.23162 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −25.5316 | −1.46193 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.3869 | −0.592810 | −0.296405 | − | 0.955062i | \(-0.595788\pi\) | ||||
−0.296405 | + | 0.955062i | \(0.595788\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.57598 | 0.146071 | 0.0730353 | − | 0.997329i | \(-0.476731\pi\) | ||||
0.0730353 | + | 0.997329i | \(0.476731\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.4844 | −0.649136 | −0.324568 | − | 0.945862i | \(-0.605219\pi\) | ||||
−0.324568 | + | 0.945862i | \(0.605219\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.1964 | −0.853514 | −0.426757 | − | 0.904366i | \(-0.640344\pi\) | ||||
−0.426757 | + | 0.904366i | \(0.640344\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.5229 | −0.813126 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.75643 | −0.320296 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 44.0159 | 2.44157 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.5316 | 0.853692 | 0.426846 | − | 0.904324i | \(-0.359625\pi\) | ||||
0.426846 | + | 0.904324i | \(0.359625\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.1062 | 0.825338 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.00866 | −0.163892 | −0.0819461 | − | 0.996637i | \(-0.526114\pi\) | ||||
−0.0819461 | + | 0.996637i | \(0.526114\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.5302 | −0.678548 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −22.8654 | −1.22748 | −0.613738 | − | 0.789510i | \(-0.710335\pi\) | ||||
−0.613738 | + | 0.789510i | \(0.710335\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.04442 | 0.484137 | 0.242068 | − | 0.970259i | \(-0.422174\pi\) | ||||
0.242068 | + | 0.970259i | \(0.422174\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.1964 | 0.968496 | 0.484248 | − | 0.874931i | \(-0.339093\pi\) | ||||
0.484248 | + | 0.874931i | \(0.339093\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −25.9556 | −1.37758 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.3869 | −1.28709 | −0.643545 | − | 0.765408i | \(-0.722537\pi\) | ||||
−0.643545 | + | 0.765408i | \(0.722537\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 31.3942 | 1.65232 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 44.5388 | 2.33127 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.86535 | −0.462768 | −0.231384 | − | 0.972863i | \(-0.574325\pi\) | ||||
−0.231384 | + | 0.972863i | \(0.574325\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.15197 | −0.163203 | −0.0816014 | − | 0.996665i | \(-0.526003\pi\) | ||||
−0.0816014 | + | 0.996665i | \(0.526003\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.5302 | 0.645337 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.28799 | −0.117526 | −0.0587631 | − | 0.998272i | \(-0.518716\pi\) | ||||
−0.0587631 | + | 0.998272i | \(0.518716\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.2509 | 1.44355 | 0.721776 | − | 0.692127i | \(-0.243326\pi\) | ||||
0.721776 | + | 0.692127i | \(0.243326\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.720669 | −0.0365394 | −0.0182697 | − | 0.999833i | \(-0.505816\pi\) | ||||
−0.0182697 | + | 0.999833i | \(0.505816\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.25223 | 0.265617 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 22.0604 | 1.10998 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.1506 | 1.06152 | 0.530759 | − | 0.847523i | \(-0.321907\pi\) | ||||
0.530759 | + | 0.847523i | \(0.321907\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.4944 | 1.42294 | 0.711472 | − | 0.702715i | \(-0.248029\pi\) | ||||
0.711472 | + | 0.702715i | \(0.248029\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.8109 | 0.538529 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.9701 | 1.08902 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.7637 | −0.532231 | −0.266116 | − | 0.963941i | \(-0.585740\pi\) | ||||
−0.266116 | + | 0.963941i | \(0.585740\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.34108 | 0.360359 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.0604 | −1.66396 | −0.831979 | − | 0.554807i | \(-0.812792\pi\) | ||||
−0.831979 | + | 0.554807i | \(0.812792\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.5833 | 1.00317 | 0.501584 | − | 0.865109i | \(-0.332751\pi\) | ||||
0.501584 | + | 0.865109i | \(0.332751\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.8553 | −0.526560 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.9629 | −1.15425 | −0.577125 | − | 0.816656i | \(-0.695826\pi\) | ||||
−0.577125 | + | 0.816656i | \(0.695826\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.9642 | 1.43999 | 0.719995 | − | 0.693980i | \(-0.244144\pi\) | ||||
0.719995 | + | 0.693980i | \(0.244144\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −45.9802 | −2.19953 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.8196 | 1.37548 | 0.687741 | − | 0.725956i | \(-0.258602\pi\) | ||||
0.687741 | + | 0.725956i | \(0.258602\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −32.0087 | −1.52078 | −0.760389 | − | 0.649468i | \(-0.774992\pi\) | ||||
−0.760389 | + | 0.649468i | \(0.774992\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −53.7293 | −2.54701 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 32.0087 | 1.51058 | 0.755291 | − | 0.655390i | \(-0.227496\pi\) | ||||
0.755291 | + | 0.655390i | \(0.227496\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.99862 | −0.376640 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.8553 | −0.975570 | −0.487785 | − | 0.872964i | \(-0.662195\pi\) | ||||
−0.487785 | + | 0.872964i | \(0.662195\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.2509 | −1.17605 | −0.588025 | − | 0.808843i | \(-0.700094\pi\) | ||||
−0.588025 | + | 0.808843i | \(0.700094\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.1520 | −0.983015 | −0.491508 | − | 0.870873i | \(-0.663554\pi\) | ||||
−0.491508 | + | 0.870873i | \(0.663554\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.9171 | −0.736554 | −0.368277 | − | 0.929716i | \(-0.620052\pi\) | ||||
−0.368277 | + | 0.929716i | \(0.620052\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 33.4028 | 1.53586 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 95.0319 | 4.36036 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.95558 | 0.0893526 | 0.0446763 | − | 0.999002i | \(-0.485774\pi\) | ||||
0.0446763 | + | 0.999002i | \(0.485774\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.9556 | −0.864300 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.48438 | −0.203625 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.9629 | 0.904604 | 0.452302 | − | 0.891865i | \(-0.350603\pi\) | ||||
0.452302 | + | 0.891865i | \(0.350603\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.0975 | −0.997247 | −0.498623 | − | 0.866819i | \(-0.666161\pi\) | ||||
−0.498623 | + | 0.866819i | \(0.666161\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.09022 | −0.139177 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.1148 | −1.48242 | −0.741212 | − | 0.671271i | \(-0.765749\pi\) | ||||
−0.741212 | + | 0.671271i | \(0.765749\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.76509 | 0.212465 | 0.106232 | − | 0.994341i | \(-0.466121\pi\) | ||||
0.106232 | + | 0.994341i | \(0.466121\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −76.7970 | −3.41742 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.7651 | 0.477154 | 0.238577 | − | 0.971124i | \(-0.423319\pi\) | ||||
0.238577 | + | 0.971124i | \(0.423319\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 30.0159 | 1.32266 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.7047 | −0.558753 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.23491 | 0.0541023 | 0.0270512 | − | 0.999634i | \(-0.491388\pi\) | ||||
0.0270512 | + | 0.999634i | \(0.491388\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.56870 | −0.374683 | −0.187342 | − | 0.982295i | \(-0.559987\pi\) | ||||
−0.187342 | + | 0.982295i | \(0.559987\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.66621 | −0.116142 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.9528 | 0.824036 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.90112 | 0.298920 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 29.5919 | 1.27937 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.0087 | −0.645273 | −0.322636 | − | 0.946523i | \(-0.604569\pi\) | ||||
−0.322636 | + | 0.946523i | \(0.604569\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.1062 | 1.03259 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.2509 | 0.523809 | 0.261904 | − | 0.965094i | \(-0.415650\pi\) | ||||
0.261904 | + | 0.965094i | \(0.415650\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.0531 | 1.15250 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −25.7810 | −1.09238 | −0.546189 | − | 0.837662i | \(-0.683922\pi\) | ||||
−0.546189 | + | 0.837662i | \(0.683922\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28.8196 | −1.21894 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.6835 | 1.04029 | 0.520143 | − | 0.854079i | \(-0.325879\pi\) | ||||
0.520143 | + | 0.854079i | \(0.325879\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 86.4115 | 3.63536 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.2335 | 0.512856 | 0.256428 | − | 0.966563i | \(-0.417454\pi\) | ||||
0.256428 | + | 0.966563i | \(0.417454\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.3126 | 1.47779 | 0.738893 | − | 0.673823i | \(-0.235349\pi\) | ||||
0.738893 | + | 0.673823i | \(0.235349\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −86.7081 | −3.61598 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.04442 | 0.376524 | 0.188262 | − | 0.982119i | \(-0.439715\pi\) | ||||
0.188262 | + | 0.982119i | \(0.439715\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −37.5906 | −1.55684 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 35.8196 | 1.47843 | 0.739216 | − | 0.673469i | \(-0.235196\pi\) | ||||
0.739216 | + | 0.673469i | \(0.235196\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.3411 | 0.961752 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −44.0617 | −1.80940 | −0.904700 | − | 0.426050i | \(-0.859905\pi\) | ||||
−0.904700 | + | 0.426050i | \(0.859905\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.0631 | 1.22835 | 0.614173 | − | 0.789171i | \(-0.289490\pi\) | ||||
0.614173 | + | 0.789171i | \(0.289490\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.1964 | 1.19095 | 0.595473 | − | 0.803375i | \(-0.296965\pi\) | ||||
0.595473 | + | 0.803375i | \(0.296965\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.1062 | −0.614153 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.1433 | −0.655237 | −0.327618 | − | 0.944810i | \(-0.606246\pi\) | ||||
−0.327618 | + | 0.944810i | \(0.606246\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.9615 | 0.443454 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 47.1162 | 1.90301 | 0.951503 | − | 0.307640i | \(-0.0995392\pi\) | ||||
0.951503 | + | 0.307640i | \(0.0995392\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.0146 | 1.53041 | 0.765204 | − | 0.643787i | \(-0.222638\pi\) | ||||
0.765204 | + | 0.643787i | \(0.222638\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.1818 | 0.489629 | 0.244814 | − | 0.969570i | \(-0.421273\pi\) | ||||
0.244814 | + | 0.969570i | \(0.421273\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 87.2741 | 3.49096 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.67487 | 0.186399 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.8640 | −0.432488 | −0.216244 | − | 0.976339i | \(-0.569381\pi\) | ||||
−0.216244 | + | 0.976339i | \(0.569381\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.19639 | 0.364948 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.4400 | −1.20231 | −0.601153 | − | 0.799134i | \(-0.705292\pi\) | ||||
−0.601153 | + | 0.799134i | \(0.705292\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −37.8640 | −1.49321 | −0.746605 | − | 0.665268i | \(-0.768317\pi\) | ||||
−0.746605 | + | 0.665268i | \(0.768317\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −36.1964 | −1.42303 | −0.711513 | − | 0.702672i | \(-0.751990\pi\) | ||||
−0.711513 | + | 0.702672i | \(0.751990\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.2509 | −0.520141 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.0975 | 0.864742 | 0.432371 | − | 0.901696i | \(-0.357677\pi\) | ||||
0.432371 | + | 0.901696i | \(0.357677\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.5229 | 0.567457 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −44.0677 | −1.71663 | −0.858316 | − | 0.513121i | \(-0.828489\pi\) | ||||
−0.858316 | + | 0.513121i | \(0.828489\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.90702 | 0.229757 | 0.114878 | − | 0.993380i | \(-0.463352\pi\) | ||||
0.114878 | + | 0.993380i | \(0.463352\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.6835 | −0.955750 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.6908 | −0.875969 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.19777 | −0.0847178 | −0.0423589 | − | 0.999102i | \(-0.513487\pi\) | ||||
−0.0423589 | + | 0.999102i | \(0.513487\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.0631 | 1.15542 | 0.577710 | − | 0.816242i | \(-0.303947\pi\) | ||||
0.577710 | + | 0.816242i | \(0.303947\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.29528 | −0.317410 | −0.158705 | − | 0.987326i | \(-0.550732\pi\) | ||||
−0.158705 | + | 0.987326i | \(0.550732\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 55.5475 | 2.12236 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 32.4327 | 1.23559 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.19639 | −0.0455129 | −0.0227564 | − | 0.999741i | \(-0.507244\pi\) | ||||
−0.0227564 | + | 0.999741i | \(0.507244\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 74.1308 | 2.81194 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.70197 | −0.0644667 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.8813 | −1.20414 | −0.602070 | − | 0.798443i | \(-0.705657\pi\) | ||||
−0.602070 | + | 0.798443i | \(0.705657\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −40.9257 | −1.54354 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.4327 | −0.804921 | −0.402461 | − | 0.915437i | \(-0.631845\pi\) | ||||
−0.402461 | + | 0.915437i | \(0.631845\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −21.2967 | −0.797566 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 53.7293 | 2.00936 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −43.2609 | −1.61336 | −0.806680 | − | 0.590989i | \(-0.798738\pi\) | ||||
−0.806680 | + | 0.590989i | \(0.798738\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 51.0159 | 1.89468 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.1818 | 0.451799 | 0.225899 | − | 0.974151i | \(-0.427468\pi\) | ||||
0.225899 | + | 0.974151i | \(0.427468\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.10755 | 0.262882 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.4486 | 0.496736 | 0.248368 | − | 0.968666i | \(-0.420106\pi\) | ||||
0.248368 | + | 0.968666i | \(0.420106\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.4254 | 0.494531 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.87264 | −0.363171 | −0.181585 | − | 0.983375i | \(-0.558123\pi\) | ||||
−0.181585 | + | 0.983375i | \(0.558123\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.5687 | −0.827965 | −0.413983 | − | 0.910285i | \(-0.635863\pi\) | ||||
−0.413983 | + | 0.910285i | \(0.635863\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.72658 | 0.246443 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.575984 | −0.0210180 | −0.0105090 | − | 0.999945i | \(-0.503345\pi\) | ||||
−0.0105090 | + | 0.999945i | \(0.503345\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.94692 | 0.216430 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.8196 | 0.829391 | 0.414695 | − | 0.909960i | \(-0.363888\pi\) | ||||
0.414695 | + | 0.909960i | \(0.363888\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.7810 | 0.717062 | 0.358531 | − | 0.933518i | \(-0.383278\pi\) | ||||
0.358531 | + | 0.933518i | \(0.383278\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.4327 | 0.412810 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.7207 | −1.03569 | −0.517847 | − | 0.855473i | \(-0.673266\pi\) | ||||
−0.517847 | + | 0.855473i | \(0.673266\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.20505 | 0.295115 | 0.147558 | − | 0.989053i | \(-0.452859\pi\) | ||||
0.147558 | + | 0.989053i | \(0.452859\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 44.0159 | 1.58110 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.8997 | 0.533839 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.0677 | −0.825425 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 72.3126 | 2.58095 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −52.6364 | −1.87628 | −0.938142 | − | 0.346252i | \(-0.887454\pi\) | ||||
−0.938142 | + | 0.346252i | \(0.887454\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.5774 | 0.695212 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.5329 | −0.621049 | −0.310524 | − | 0.950565i | \(-0.600505\pi\) | ||||
−0.310524 | + | 0.950565i | \(0.600505\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.70335 | −0.0956375 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 39.5833 | 1.39686 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.15059 | −0.251401 | −0.125701 | − | 0.992068i | \(-0.540118\pi\) | ||||
−0.125701 | + | 0.992068i | \(0.540118\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.6835 | −1.11256 | −0.556280 | − | 0.830995i | \(-0.687772\pi\) | ||||
−0.556280 | + | 0.830995i | \(0.687772\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −74.1679 | −2.59799 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −62.2224 | −2.17689 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.0690 | −0.525913 | −0.262956 | − | 0.964808i | \(-0.584698\pi\) | ||||
−0.262956 | + | 0.964808i | \(0.584698\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.9556 | −0.730465 | −0.365233 | − | 0.930916i | \(-0.619011\pi\) | ||||
−0.365233 | + | 0.930916i | \(0.619011\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.7897 | 1.27930 | 0.639652 | − | 0.768665i | \(-0.279079\pi\) | ||||
0.639652 | + | 0.768665i | \(0.279079\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.3053 | 1.60825 | 0.804125 | − | 0.594460i | \(-0.202634\pi\) | ||||
0.804125 | + | 0.594460i | \(0.202634\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 59.8414 | 2.07090 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.6377 | −0.885113 | −0.442556 | − | 0.896741i | \(-0.645928\pi\) | ||||
−0.442556 | + | 0.896741i | \(0.645928\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.4771 | −0.499210 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.38688 | 0.322918 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 37.3411 | 1.28004 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.43130 | −0.185964 | −0.0929821 | − | 0.995668i | \(-0.529640\pi\) | ||||
−0.0929821 | + | 0.995668i | \(0.529640\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.23491 | 0.247140 | 0.123570 | − | 0.992336i | \(-0.460566\pi\) | ||||
0.123570 | + | 0.992336i | \(0.460566\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.43130 | −0.185314 | −0.0926568 | − | 0.995698i | \(-0.529536\pi\) | ||||
−0.0926568 | + | 0.995698i | \(0.529536\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.7120 | 0.364641 | 0.182320 | − | 0.983239i | \(-0.441639\pi\) | ||||
0.182320 | + | 0.983239i | \(0.441639\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −39.2064 | −1.33306 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.6058 | 0.665083 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.5833 | −0.392484 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.8168 | −0.466560 | −0.233280 | − | 0.972410i | \(-0.574946\pi\) | ||||
−0.233280 | + | 0.972410i | \(0.574946\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.6662 | 0.797335 | 0.398667 | − | 0.917096i | \(-0.369473\pi\) | ||||
0.398667 | + | 0.917096i | \(0.369473\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.9615 | 0.638105 | 0.319052 | − | 0.947737i | \(-0.396635\pi\) | ||||
0.319052 | + | 0.947737i | \(0.396635\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.3955 | 0.684815 | 0.342408 | − | 0.939552i | \(-0.388758\pi\) | ||||
0.342408 | + | 0.939552i | \(0.388758\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 23.6662 | 0.791959 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −73.1606 | −2.44549 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.5302 | 0.417905 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.99862 | −0.266473 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 70.4944 | 2.34331 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40.0146 | 1.32866 | 0.664331 | − | 0.747439i | \(-0.268717\pi\) | ||||
0.664331 | + | 0.747439i | \(0.268717\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.8268 | 0.424972 | 0.212486 | − | 0.977164i | \(-0.431844\pi\) | ||||
0.212486 | + | 0.977164i | \(0.431844\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.52428 | 0.215922 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43.9542 | −1.44992 | −0.724958 | − | 0.688793i | \(-0.758141\pi\) | ||||
−0.724958 | + | 0.688793i | \(0.758141\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 19.9025 | 0.655099 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −77.1766 | −2.53755 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −40.2349 | −1.32006 | −0.660032 | − | 0.751237i | \(-0.729457\pi\) | ||||
−0.660032 | + | 0.751237i | \(0.729457\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.2509 | −0.433349 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.06175 | −0.100023 | −0.0500114 | − | 0.998749i | \(-0.515926\pi\) | ||||
−0.0500114 | + | 0.998749i | \(0.515926\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.1891 | −0.658146 | −0.329073 | − | 0.944304i | \(-0.606736\pi\) | ||||
−0.329073 | + | 0.944304i | \(0.606736\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.5947 | −0.442704 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.14468 | 0.0371973 | 0.0185986 | − | 0.999827i | \(-0.494080\pi\) | ||||
0.0185986 | + | 0.999827i | \(0.494080\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −34.1520 | −1.10862 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42.9701 | −1.39194 | −0.695970 | − | 0.718071i | \(-0.745025\pi\) | ||||
−0.695970 | + | 0.718071i | \(0.745025\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.7047 | −0.411115 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.1891 | −0.651262 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 74.7453 | 2.40614 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.99862 | 0.321534 | 0.160767 | − | 0.986992i | \(-0.448603\pi\) | ||||
0.160767 | + | 0.986992i | \(0.448603\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.6291 | −1.04712 | −0.523558 | − | 0.851990i | \(-0.675396\pi\) | ||||
−0.523558 | + | 0.851990i | \(0.675396\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −41.4958 | −1.32757 | −0.663784 | − | 0.747924i | \(-0.731051\pi\) | ||||
−0.663784 | + | 0.747924i | \(0.731051\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −47.7512 | −1.52613 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −35.4327 | −1.13013 | −0.565063 | − | 0.825047i | \(-0.691148\pi\) | ||||
−0.565063 | + | 0.825047i | \(0.691148\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −44.1148 | −1.40562 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 56.7724 | 1.80526 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48.5919 | −1.54357 | −0.771787 | − | 0.635881i | \(-0.780637\pi\) | ||||
−0.771787 | + | 0.635881i | \(0.780637\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 30.0159 | 0.951569 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 47.0260 | 1.48933 | 0.744664 | − | 0.667440i | \(-0.232610\pi\) | ||||
0.744664 | + | 0.667440i | \(0.232610\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5292.2.a.u.1.1 | 3 | ||
3.2 | odd | 2 | 5292.2.a.x.1.3 | 3 | |||
7.2 | even | 3 | 756.2.k.f.109.3 | yes | 6 | ||
7.4 | even | 3 | 756.2.k.f.541.3 | yes | 6 | ||
7.6 | odd | 2 | 5292.2.a.w.1.3 | 3 | |||
21.2 | odd | 6 | 756.2.k.e.109.1 | ✓ | 6 | ||
21.11 | odd | 6 | 756.2.k.e.541.1 | yes | 6 | ||
21.20 | even | 2 | 5292.2.a.v.1.1 | 3 | |||
63.2 | odd | 6 | 2268.2.l.k.109.3 | 6 | |||
63.4 | even | 3 | 2268.2.l.j.541.1 | 6 | |||
63.11 | odd | 6 | 2268.2.i.j.2053.1 | 6 | |||
63.16 | even | 3 | 2268.2.l.j.109.1 | 6 | |||
63.23 | odd | 6 | 2268.2.i.j.865.1 | 6 | |||
63.25 | even | 3 | 2268.2.i.k.2053.3 | 6 | |||
63.32 | odd | 6 | 2268.2.l.k.541.3 | 6 | |||
63.58 | even | 3 | 2268.2.i.k.865.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.k.e.109.1 | ✓ | 6 | 21.2 | odd | 6 | ||
756.2.k.e.541.1 | yes | 6 | 21.11 | odd | 6 | ||
756.2.k.f.109.3 | yes | 6 | 7.2 | even | 3 | ||
756.2.k.f.541.3 | yes | 6 | 7.4 | even | 3 | ||
2268.2.i.j.865.1 | 6 | 63.23 | odd | 6 | |||
2268.2.i.j.2053.1 | 6 | 63.11 | odd | 6 | |||
2268.2.i.k.865.3 | 6 | 63.58 | even | 3 | |||
2268.2.i.k.2053.3 | 6 | 63.25 | even | 3 | |||
2268.2.l.j.109.1 | 6 | 63.16 | even | 3 | |||
2268.2.l.j.541.1 | 6 | 63.4 | even | 3 | |||
2268.2.l.k.109.3 | 6 | 63.2 | odd | 6 | |||
2268.2.l.k.541.3 | 6 | 63.32 | odd | 6 | |||
5292.2.a.u.1.1 | 3 | 1.1 | even | 1 | trivial | ||
5292.2.a.v.1.1 | 3 | 21.20 | even | 2 | |||
5292.2.a.w.1.3 | 3 | 7.6 | odd | 2 | |||
5292.2.a.x.1.3 | 3 | 3.2 | odd | 2 |